A Multiscale Mathematical Model for Tumor Growth, Incorporating the GLUT1 Expression.

We propose a multiscale mathematical model for the avascular tumor growth. At the cellular scale, the model takes into account the biochemical environment, the different phases of the tumor cell cycle, the cells signaling, and cellular mechanics through a bioenergetics approach. A mathematical function is employed, namely, the "health function," that stands for the cells' biochemical energy in tumor's different regions, with respect to the carrying capacity of the extracellular matrix (ECM) and the metabolic processes of tumor cells. We also encounter in the model the glucose transporter GLUT1. The role that it plays in mitosis is investigated for the different kinds of tumor cell populations, as its overexpression in malignant cells is associated with the disease development. Simulations have been made, scaling up and estimating the evolution of tumor cell populations. By incorporating biochemical processes in tumor growth multiscale modeling, we aim to provide better understanding of the disease and assessment of possible targeted therapeutic strategies.